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arXiv · 0706.1046

Multiscale expansion of the lattice potential KdV equation on functions of infinite slow-varyness order

Rafael Hernandez Heredero·Decio Levi·Matteo Petrera·Christian Scimiterna
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Abstract

We present a discrete multiscale expansion of the lattice potential Korteweg-de Vries (lpKdV) equation on functions of infinite order of slow-varyness. To do so we introduce a formal expansion of the shift operator on many lattices holding at all orders. The lowest secularity condition from the expansion of the lpKdV equation gives a nonlinear lattice equation, depending on shifts of all orders, of the form of the nonlinear Schr\"odinger (NLS) equation

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Rafael Hernandez Heredero, Decio Levi, Matteo Petrera, Christian Scimiterna. 2007-06-07. Multiscale expansion of the lattice potential KdV equation on functions of infinite slow-varyness order. https://doi.org/10.1088/1751-8113/40/4/017

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